Data-driven sparse identification of nonlinear dynamical systems using linear multistep methods

主讲人：陈浩

摘要：Linear multistep methods (LMMs) are popular time discretization schemes for solving the forward problem on differential equations. Recently, LMMs together with deep neural networks have been shown to successfully discover dynamical systems from data. In this work, we propose a class of LMM-based sparse regression approaches for the discovery of nonlinear dynamical systems. The work builds on the sparse identification of nonlinear dynamics (SINDy) framework presented in [S. L. Brunton, J. L. Proctor, J. N. Kutz, Proc. Natl. Acad. Sci. 113 (2016) 3932--3937], allowing closed form expression for the governing equations and therefore the resulting data-driven model can give insights into the underlying physics. Compared to the standard SINDy algorithm, the proposed LMM-based SINDy approach allows for more accurate and robust model recovery from data with a wide range of noise levels, without requiring pointwise derivative approximations and conventional noise filtering. Numerical results are presented to demonstrate the effectiveness of the proposed method.

主讲人简介：陈浩，博士， 现为重庆师范大学数学科学学院教授、硕士生导师，中国仿真算法专业委员会委员。主要从事微分方程数值解及数值线性代数研究，主持过国家自然科学基金及省级科研项目多项，在《J. Comput. Phys.》、 《Numer. Linear. Alge. Appl.》、 《BIT》、 《J. Sci. Comput.》等计算数学重要刊物上发表科研论文30余篇。

邀请人：张诚坚

时间：2024年4月19日（星期五）10:00-12:00